Question

For f(x) = 2x + 1 and g(x) = x^2 - 7, find (f-g)(x)

Answer 1

Answer:

$\displaystyle (f - g)(x) = -x^2 + 2x + 8$

Step-by-step explanation:

We are given the two functions:

$\displaystyle f(x) = 2x + 1 \text{ and } g(x) = x^2 - 7$

And we want to find:

$\displaystyle (f- g)(x)$

Recall that:

$\displaystyle (f - g)(x) = f(x) - g(x)$

Substitute and simplify:

$\displaystyle \begin{aligned}(f-g)(x) &= f(x) - g(x) \\ \\ &= (2x + 1) - (x^2 - 7) \\ \\ &= (2x +1 )+ (-x^2 + 7) \\ \\ &= -x^2 +2x + 8\end{aligned}$

In conclusion:

$\displaystyle (f - g)(x) = -x^2 + 2x + 8$